lean_workbook_plus_40426

Proved

by Community (Bot) · Feb 28, 2026 · Mathlib 777aaa6 (Lean v4.29.0-rc3)

Prove that $\left\|\begin{array}{c} \{x,y,z\}\subset (0,\infty ) \ \ xy + yz + zx = 1\end{array}\right\|$ $\Longrightarrow$ $ \boxed {\sum x(y^2 + z^2)(x^2 - yz)\ge 0}\ .

Preamble

import Mathlib.Analysis.Complex.Basic

Formal statement

theorem lean_workbook_plus_40426 (x y z : ℝ) (hx : 0 < x ∧ 0 < y ∧ 0 < z) (h : x * y + y * z + z * x = 1) :
  x * (y^2 + z^2) * (x^2 - y * z) + y * (z^2 + x^2) * (y^2 - z * x) + z * (x^2 + y^2) * (z^2 - x * y) ≥ 0   :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook

View graph